Gleason solutions and canonical models for row contractions

Master Thesis

2017

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http://hdl.handle.net/11427/25491
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thesis_sci_2017_ramanantoanina_andriamanankasina.pdf (1.2 MB)
Authors
Ramanantoanina, Andriamanankasina
Supervisors
Martin, Robert T W
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University of Cape Town

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Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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Abstract
This thesis extends the deBranges-Rovnyak model for completely non-coisometric (CNC) contractions to the setting of row contractions from several copies of a Hilbert space into itself. It is shown that a large class of of row contractions (including all CNC row contractions with commuting components) can be represented as extremal Gleason solutions in the de Branges-Rovnyak space associated to a contractive multiplier between vector-valued Drury-Arveson spaces. Here, a Gleason solution is the appropriate several-variable analogue of the adjoint of the restricted backward shift. Given such a row contraction T, the corresponding multiplier bT , that is, the characteristic function of T, is shown to be unitary invariant. We further characterise a natural sub-class of row contractions for which it is a complete unitary invariant.
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Mathematics

Reference:

Ramanantoanina, A. 2017. Gleason solutions and canonical models for row contractions. University of Cape Town.

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